You visited us 1 times! Enjoying our articles? Unlock Full Access!

Centripetal Force

A small block...

Question

A small block of mass $m_{3} = 2 k g$ of negligible size is placed on a plank of mass $m_{2} = 4 k g$ and length 4m which is further placed on a frictionless surface as shown in figure. If $m_{1} = 8 k g$ and system starts from rest,

Time after which

m_{3}

falls from

m_{2}

\infty

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Time after which

m_{3}

falls from

m_{2}

is 2 sec

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Velocity of

m_{1}

at 2 sec is 12 m/s

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Velocity of

m_{2}

at t = 2 sec is 11.4 m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
B Time after which $m_{3}$ falls from $m_{2}$ is 2 sec
C Velocity of $m_{1}$ at 2 sec is 12 m/s
Assume all the blocks move together, then $a = \frac{m_{1} g}{m_{1} + m_{2} + m_{3}}$
$= \frac{80}{8 + 4 + 2} = \frac{80}{14} = 5.7 m$
Friction acting on $m_{3} = m_{3} a = 2 \times 5.7$
$= 11.4 N$
But maximum friction on $m_{3}$ can only be, $f = m_{3} g μ = 20 \times 0.4 = 8 N$
Therefore, $m_{3}$ sliding on $m_{2}$ , and $f = 8 N$

$a = \frac{m_{1} g - f}{m_{1} + m_{2}} = \frac{80 - 8}{12} = 6 m / s^{2}$

acceleration $(a_{0})$ of $m_{3}$ is $a_{0} = \frac{f}{m_{3}} = \frac{8}{2} = 4$
Relative acceleration of $m_{3}$ with respect to $m_{2}$ is $6 - 4 = 2 m / s^{2}$
The distance it has to cover is 4m.
$∴ s = u t + \frac{1}{2} a t^{2}$
$4 = \frac{1}{2} \times 2 \times t^{2}$
$\Rightarrow t = 2 s e c$
Velocity of $m_{1}$ and $m_{2}$ at t = 2 sec is $u + a t$
$= 0 + 6 \times 2 = 12 m / s$

Suggest Corrections

Similar questions

Q. A small block of mass

m_{3} = 2 k g

of negligible size is placed on a plank of mass

m_{2} = 4 k g

and length 4m which is further placed on a frictionless surface as shown in figure. If

m_{1} = 8 k g

and system starts from rest,

Three solids of masses $m_{1}, m_{2} a n d m_{3}$ are connected with weightless string in succession and are placed on a frictionless table. If the mass $m_{3}$ is dragged with a force T, the tension in the string between $m_{2}$ and $m_{3}$ is

Q. A wedge of mass

m_{3}

is placed on a smooth horizontal surface. Blocks of mass

m_{1} and m_{2}

are placed on the smooth inclined faces of

m_{3}

as shown. If

m_{3}

does not move, the ratio

\frac{m_{2}}{m_{1}}

is equal to

Q. Three blocks are connected as shown in figure and placed on a horizontal frictionless surface if

m_{1} = 2 k g, m_{2} = 8 k g

and

m_{3} = 27 k g

and

T_{3} = 37 N

then ratio of

T_{2} / T_{1}

Q. Four blocks of masses

M_{1}, M_{2}, M_{3}

and

M_{4}

are placed on a smooth horizontal surface along a straight line as shown above. It is given that

M_{1} >> M_{2} >> M_{3} >> M_{4} .

All the blocks are initially at rest.

M_{1}

is given initial velocity

v_{0}

towards right such that it will collide with

M_{2} .

Consider all collisions to be perfectly elastic. The speed of

M_{4}

after all collision are over is

Join BYJU'S Learning Program

A small block of mass m3=2kg of negligible size is placed on a plank of mass m2=4kg and length 4m which is further placed on a frictionless surface as shown in figure. If m1=8kg and system starts from rest,

A small block of mass $m_{3} = 2 k g$ of negligible size is placed on a plank of mass $m_{2} = 4 k g$ and length 4m which is further placed on a frictionless surface as shown in figure. If $m_{1} = 8 k g$ and system starts from rest,